Vocal bursts play an important role in communicating affect, making them valuable for improving speech emotion recognition. Here, we present our approach for classifying vocal bursts and predicting their emotional significance in the ACII Affective Vocal Burst Workshop & Challenge 2022 (A-VB). We use a large self-supervised audio model as shared feature extractor and compare multiple architectures built on classifier chains and attention networks, combined with uncertainty loss weighting strategies. Our approach surpasses the challenge baseline by a wide margin on all four tasks.